There is not a single meaning to the word "okay" in Cormac McCarthy's book The Road. The word is used nearly 200 times in the text, and the word has multiple functions throughout the story. The reason for that is because "okay" can function as a verb, adjective, adverb, or even a noun. The first time that readers encounter an "okay" exchange between the father and the son "okay" is used to express agreement. It is equivalent to "sounds good" or "I'll go with that."

I'm going to blow out the lamp. Is that okay?
Yes. That's okay.

There are times when "okay" carries a different meaning and message. The man clearly loves the boy, and the boy clearly loves his father; however, the two don't always see eye to eye on everything. The man doesn't trust anybody, and he isn't willing to risk his son's life to test any of that trust. The boy is much more willing to reach out and help people, and this is often a point of contention between the two characters. They will argue with each other at times, and "okay" sometimes is not expressing agreement. Sometimes it is expressing disagreement and the desire not to continue a conversation. "Okay" can mean "drop it, I don't want to talk about it anymore."

He's going to die. We cant share what we have or we'll die too.
I know.
So when are you going to talk to me again?
I'm talking now.
Are you sure?
Yes.
Okay.
Okay.